Never repair a large hole or one that's in the sidewall. It isn't safe and could lead to a dangerous blowout. A plug by itself, or a patch by itself, is not acceptable. But a safer tire repair, done to the RMA standards, can give you thousands of miles more use from your tire.
Secondly, how do you fix a leaking lawn mower tire?
Moreover, is it better to patch or plug a tire? Patches are better than plugs for bigger holes, holes closer to but not the sidewall and holes that aren't completely straight. Note that if you're looking to do tire sidewall repair, a patch will usually not cut it and you'll likely want to replace the tire. Don't patch the tire if it's near the sidewall.